# Relaxation-assisted reverse annealing on nonnegative/binary matrix factorization

## TL;DR

This paper introduces a new method combining quantum-inspired reverse annealing with classical relaxation techniques to improve matrix factorization performance in machine learning.

## Contribution

The novel integration of reverse annealing with linear programming relaxation improves optimization performance in nonnegative/binary matrix factorization.

## Key findings

- The proposed method achieves better convergence on facial image datasets compared to existing reverse annealing methods.
- Relaxation-based initialization shows a relationship between relaxed and optimal solutions on randomized datasets.
- Combining reverse annealing with classical optimization strategies enhances overall optimization performance.

## Abstract

Quantum annealing has garnered significant attention as meta-heuristics inspired by quantum physics for combinatorial optimization problems. Among its many applications, nonnegative/binary matrix factorization stands out for its complexity and relevance in unsupervised machine learning. The use of reverse annealing, a derivative procedure of quantum annealing to prioritize the search in a vicinity under a given initial state, helps improve its optimization performance in matrix factorization. This study proposes an improved strategy that integrates reverse annealing with a linear programming relaxation technique. Using relaxed solutions as the initial configuration for reverse annealing, we demonstrate improvements in optimization performance comparable to the exact optimization methods. Our experiments on facial image datasets show that our method provides better convergence than known reverse annealing methods. Furthermore, we investigate the effectiveness of relaxation-based initialization methods on randomized datasets, demonstrating a relationship between the relaxed solution and the optimal solution. This research underscores the potential of combining reverse annealing and classical optimization strategies to enhance optimization performance.